Hob



oct, 3o, 192s.`

N. TRBOJEVICH HOB Filed Jan.

28, 1924 4 sneetssheet -ttomurg N. TRBOJEVICH Oel;v 30, 1928.

HOB

Filed Ja`n. 28.- 1924 4 Sheets-Sheet v @noem/01,

- attorneys manica oa.'4 3o, 192s.

, hobs used in my s process U. S. in

y 1,689,566 PATENT. ori-ica arizona "rnnoinvicn, on ./nn'rlnornMICHIGAN, AssIGNon To GnEAsoN wonxs, or

ROCHESTER, NEW'YORK, A. CORPORATION OF NEW YORK.

l non Application ledJanua'ry 28,l 1924.

The invention relates l to a novel forni of hob or gear cutter andparticularly to a novel form of hob, or gear cutter ofthe spiral crownwheel type. The new hobs are used principally for the generation oftapered worms of stance, the` blanks from which the taperedPat.41,465,150) are made, or the worms which runin mesh with the newspiral hyperboloidal gears described in mycopending application SerialNumber 684,862,

filed January 7, 1924. Another object of the invention is' to provide acutting tool capable of generating the common or spur worms and screws.Further objects will be apparent hereinafter from'thedescription. andthe ap- The' method according to pended claims. which, and the'apparatus in which, the newhobs may be employed in practice, are fullydescribed intanother copending application, and the present applicationis devoted` solely to the description of-the cutting tool or, hob. Thenew hob has two modifications, both of a similar geometrical form, butdifferent as to theircorresponding physical characteristics,-

v viz the steel hob p which is made usually of high speed steel andprovided .with a definite number ofpermanent'cutting teeth, and thegrinder hob, composed of einery or some' other abrasive material, andpossessing practically an indefinite number of cutting particles. Inthe'following' description it will be disclosed first how the new hobsm'ay be calculated and designed 'with reference to the work to beperformed, second, how they can be accurately manufactured, and third,how they are sharpened or dressed and kept in proper working conditionwhen in `actual use. Thus, in the case of grinder hobs we grinders mayaccurately and comparatively easily be' dressed to the proper spiralcontour by mechanical means and vas voften asvit may be required.

In the drawings Figure lis a plan viewof a preferred form Figure 2 s atransverse section thereof;

' Figures plauatory of the theory ofthe process i F igures and 9 are thepitch plane sections illustrating the generation of the tapered and spurworms respectively;

FigureslO to 13 are'diag'rams illustrating constant pitch, such as are,fonin iral bevel gear hobbing.

shall show how such V 4, 5, 6, '7, and` 8 are diagrams ex .abridgedSerial No. A689,13'1.

the method of trimming the contour of the new grinder hob.

These hobs are used principally, as stated, in the production of worms.In order to understand the principle upon which the new hobs operate, itis necessary to become ac" 'quainted with4 forming the foundation ofthis system of wormcutting. f f

yFigure 1""'and Figure,2 show two views of the new hob of the modiedinvolute crown wheel type. Said hob -consists primarily of a circularflatdi-sk A upon the plane face of which one or more convolutions ofcutting teeth B are spirally arranged, said spirals d2 having themathematical equation.

coordina-te system shown in Figure l, an termine a spiral which I termeda modified involute of a circle. A superficial analysis of said twoequations willdisclose the fact that besides the two variablecoordinates :v1 y and "the variable parametric angle 2 the'equationsalso contain two constants a and p, respectively designated as the ba-seradius and the modification of the spiral.

In manufacturing the new hobs, a circular disk A is first turned andbored. Next, the blanlis mounted in a universal milling machine and theconvolutions B are milled by gearing up said milling machine to a leadequal to 2am, the circumference of the circle C2 of the hob, and byplacing va rotary end mill G in the yline b, said'line being offset fromthe distance equal to of the hob. It can be shown mathematically that ifthe hob is translated along the line b (whichiine coincides. with therack element of the hob) and also the mathematical peculiaritiesvdderotated in a timed relation in the proper direction any fixed point Ein the' line scribe a modified involute defined by the equations (l)upon the face of the hob. These modified involutes willv be of theextended type if the value of p is positive, that is, if the amount ofoffsetting (0H-p) is greater than the base radius of hob, and they willbe involutes for all negative values of p. It is of interest to notethat the modified fin'volute may de enerate into a commoninf lar totheplane o use, and fifth, rthe number of flutes is a rela'. l

i' ds forming the-flutes of the crown hob of the.

' extended 'lnvolute t Ivolute for ,the va angles, third vchanicallfy,that is by means of a relieving Aoperation in the manufacture ue of p=o,and also into an Archimedean spiral for a+ p=o. We shall show, however,that for the purposes of producing the hob or worm specificallydescribed in the vabove mentioned applications both p and a-l-p mustalways be different from zero and finite. l

After the required number of convolutions B have been milled, and theirsides have been beveled off to the required pressure angle a (Figure 2)so that the cross section of the hob thread along the line I) presents arack of constant pitch, said convolutions are gashed crosswise bya'number of equi-spaced flutes b1 b2 etc., and the remaining portions ofthe thread are relievedby means of a. suitable relieving tool in adirection perpendicular to the plane of the hob as shown at I-I, Figure2. In Figure 1 the flutes are all straight and,

are tangent to the (cz-tp) circle, which arrangement ispreferable-providing the distance p is small in comparison with thediam`v eter of the hob. However, if the dista-nce p 1s considerable, theflutes are preferabl curved in order that the cutting faces of teet maybe more nearlylperpendicular to the 'will correctly mesh with saidArchimedian thread spirals. In Figure 3 such an arrangement isdiagrammatically shown. There the spirals are extended involutes Z2while the flutes are-abridged involutes d3 so selected that they areperpendicular to the hob spiralsl d2 at the point I, said point lyingsubstantiallg inthe middle of the cutting face of the hob. egarding theselection, and general arrangement of flutes in the new hobs it may bestatedthat theoretically, any kind of' flutes may be employed, straightor spiral, equally or unequally spaced. In practice, however, the flutesare usually. so selected that first they are equally s aced, secondtheyV intersect the thread convoliutions at approximately right the hobsmaybe relieved metool reciprocatinnl in a` direction perpendicuthe hobat a constant ratio, fourth, the finished hobs maybe accuratel isharpened after they become dull -throug tive prime number with respecttothe total number of convolutions or leads in the hob.,

' Thus it may be seen that in providingthe new hobs with suitableflutes, preferably the same' precautions are applied as in the case ofcommon or spur hobs. l, 4

'JThe dimensions of the abridged involutes n pe ,shownl in Figure 3, areso selectedthat vt e relieving tool may recipr'ocate or jump in a timedrelation withthe rotation ofthe hob during the relieving or 'whatis'sometimes termed, the backing-off of such hobs,

and may be determined from the triangle IJ. The modification po'f.saidinvolute is y publications.

equal to the distance DlJvwhilethe base rathe line b is' constant andequal t0 2a1r. I.

Thus the new hobs may be manufactured with an 'extreme accuracy, as thecuttin teeth may -be milled, gashed, relieved,l and also peredfworm A,Figure l and Figure 3 is de-i veloped in a plane,- the longitudinaltooth principle curves become spirals of constant lead (Archimedeanspirals) Z1 the mathemati-cal equation of which in nates is obviously:

'where is the base radius orI the 'so called polar subnormal of the wormspiral.

It is now desired to construct a spiral that spiral at a constant ratio.The new spiral must be a modified involute as defined by the equations(l), and'I have proved that 'fact mathematically in my former patentsand Said fact is also fairly obvious from purely kinematicalconsiderations. -Because when the line b to which the-.rack gen,

erator b is rigidly attached is rolled without slipping on thecircumferen e of the (l1-circle, the lpoint E on the line b willchimedean spiral d1. However, when the parallelogram Z bis rolled on thecircle C2 the curve described by the describe the Ar-4 point E is theexthe XlY1 system of coorditended involute d2, according to thedefinition of that spiral. Hence, the two, spirals d1v and d, are whatmight be termed odontieally conjugate to each other (being generated bythe same lines rolling on twotangent circles) and their common normalsin any position must pass through the pitch point F -of the system,while thelocus'rof points ofl tangency (the line of action isy the lineb.

Therefore, when the two base circles C1 and 'Cz'.rtoll together like thepitch circles of two s ur albng the line b with a constantvelocity andthe spiral d2 will generate the spiral d1'(or vice versa) in its fulllength. It is also evident that in ordcrvto insure the continuity ofengagement for any number of revolutions, the spirals d, must be equallyspaced wit-h res ect to the center D2', and said spacing (in t e aremeasure of the base circle C2) gears, the point E will be translatedlarrbe exactly equal to` the pitch of the worm to' i be generated. Thus,in order to insure the continuous and correct meshing between thetapered, worm A, and the crownhob A the v values of a and p,

following two relations determining the and therefore, the spiralitself, must necessarily exist:

wher frz/1 and n., are the number of threads or convo utions in thetapered worm and crown hob r spectiyely, is the pitch cne angle of the wrm and p0 is the pitch of the rack generato b. Hence, the hob spiral ispartially deter ined from the dimensions of the worm to be generated,and becomes fully determined when the number of convolutions in hob n,is selected. In selectingthe number n, it is advisable to select it sothat it be relatively prime to 11,1, in order to' obtain the smoothcstfinish of the tooth surfaces obtainable with a given (limited) numberlof liutes or gashes.

Referring now a ain to the'example illustrated in Figure 1 and Figure 2,there the worm, A, hasacone angle of 30 degrees and is single threaded,6 diametral pitchi Therefore, from tlce equation (3) the distance p,becomes one sixth of an inch. The hob has six threads (of which fourwere milled away to facilitate the manufacture) and has a base radius(calculated from the "equation (4), a-:l/Z inch. The hob is providedwith 35 utes, said number being relatively prime to six, and six again aprime with respect to one,

.the number of threads in the worm. The

above numerical data serves merely to demonstrate one of the manypractical applications vof the'kinematical laws which I havediscovered,and in no way limits the scope olf-this invention.

ln Figure 8 the worm to be generated is multiple threaded, having alconsiderable angle FTD,==, and the hob is spirally fluted. Tt isinteresting to` note the shaded areas elements with their common tangentplane, or Athe pitch plane. The teeth B of the hob p are relievedthereby forming suitable cuttingedges along the spiral flutes' d3, alongwhich the hob also may be sharpened without xafecty -ing the correctspacing or formof the cutting teeth when it becomes dull. The crescentshaped cross sections B1 of the worm thread are concave andcomparatively i'at on their sides facing the apex D1 and arepronouncedlyconvex on the other side. This geometrical peculiarity insures thecorrect\ action of the' ments is thereby localized along the line b (asrequired by the theory) and the mutilation of .the worm threads isavoided by the hob threads may pass through the series of equi-spacedlcrescents without touching the cross sections of the twoy 'definition othe circular discrepancy,

the Contact between the two elel the fact that'` according tothe theory,

rack element `is constant alongfthe line yfand y them at any otherpoints except those lyingv in the line b.

- A graphical method of v exact shape of any crescent B1 (such as areshown in Figure 3) is shown in Figure 5 and Figure 6. Itis seen that thecurvature of said segment ismaterially iniuenced by the pressure angle aof the worm. Thus, in order to avoid interference and multilation of theworm threads, a pressure angle sufficiently great, ranging from 15 to 30degrees is preferably employed. L

The process of generating of constant lead by means of'new hobs may nowbe mapped out. The hob spiral 1s first calculated and made up as alreadydiscussed.

The tapered worm blank is superposed upon determining the tapered wormsthe hob so that its rack generator coincides with the rack element b andits apex with the point D1, Figure '3. Next the two elements are rotatedin a timed relation and the blank is also given a relative movement oftranslation or feed in a line perpendicular to .the .'tace'of the hob. ii

The process of generating cylindrical or spur worms will best beunderstood from the Figures 7 8 and 9. The intersections ol' the wormthread B3 with a system of planes m,

'm1, fm2, all parallel to the axis of the worm, are

the elliptical contours M, M1, M2. Those contours are more fully shownin Figure 9 where also their engagement with an extended in' voluteconvolution d, is illustrated. It is seen that if the crown cientlylarge radius of curvature (greater than the radius of the ellipticcontours M) a condition. maybe established in which the contact betweenthe two elements always falls in the line Z), and the thread of the hobis veryl nearly tangent to the helixes of the worm to be generated. Now,when the hob is rotated with a uniformvelocity, its imaginary rackelement moves also with .a uniform velocity along the line b, as this isthe definition ofthe modified involute.A On rotary worm blank A3possesses a similar characteristic, according to the well Vknown helix.Thusthe two elements ,will correctly mesh providing the discrcpancybetween the initial and nal acute anglesllf2 and 1,!11, 9) is not toogreat. As shown in Figure 9 only one threadconvolut-ion d, isemployedyin the hob for the purpose of minimizing said and in consequence, only ashort length of the blank A3 is being machined (the hob possesses asulla the other hand, the

respectively (Figure section extending from E2 to E1) at a time.

However, worms of considerable length may be produced ita slowtangential feed movement is imparted to the blank'A3 alongr the line bduring the may be done without departing from the principle of theuniformlyttimed movements, as thelf'yelocity Lofthe process ofgeneration. This any uniform translation ofthe whole blank alongsaid'line is convertible into `and com-- pensable by, a suitableincrement of rotation imparted to the hob.

The abrasive crown hobsx In the practical application of this processhobs are made of 'some suitable abrasive material such as emery,carborundum, etc., and are first roughly molded into a spiral shapeofthe modified involute type. After the grinder is mounted upon its arborand properly balanced, itfis dressed to thel exactoshapeby f means of arapidly rotating diamond trimmer.

The method of. dressing the spiral grinder `her-ein described is basedupon a new principle of wheel dressing fully described in my copendingapplication for Patent Serial Number 647,670', filed- June 25, 1923. Ac-

cording to that principle the grinding wheel 83 (Figures 10, l1', v12,'and ,13) while being dressed is rotated very slowly, and the trim?m'er-damond`l'34r very rapidly. In this mann er it is possible'toproduce helical and spiral convolutions upon the cutting surface of thewheel with av great precision, and in a reason- -able length of time, asthe wheel while being slowly rotated may also be translatedsalong acertain fixed line (such as the' line b Figure 11) in a `timed relation,and exact spirals,

'heliXes and other mathematical curves and surfaces thus may begenerated.

Figure 10 is the cross section of the arlrangement shown in Figure V11.through the tol ^ true contour of the line b. The diamond 85 is held inthe end ofthe stud 86 in the trimmer spindle 84' and capable of rapidlydescribing the circles 87. Saidcircle is so selected that it approachesthe modified involute convolution d, as closely as possible. When thegrinder 83 is slowly rotated and also trans-.

lated in a timed relation along the line b, the diamond 85 will describea series of .circles 87 shown in detail in Figure 12) and .thereby ressthe surface of the entire convolution d2. A modification offthe abovedressing process is diagrammatically shown 4in Figure 13; 'Therethe-grinder 83 is lnot directly in contact with the diamond 85, as firstan intermediate small cylindrical wheel 88 4made of a harder substancethan the main grinder 83,

is dressed first by reciprocating thediamond wheel 83 is trimmed bymeans of said4 auxil-` iary or-intermediate wheel 88; It isto be 85 asshown lby the arrows, and then the main V notedfthat the-wheel 88rotates very rapidly,

' and the' Wheel 831comparatively-slawly, and" preferabl in an oppositedirection.

Thus tie grinding operation. in thissysl tem of worm manufacturing iskinematically similar tovl .the milling ,oper-ation in all fre# spects.except that `first the generating machine is run ata much higher rate ofspeed, second, the generating utteror hob possesses a practicallyindefinite number of easily-.destroyed cutting edges or particles, andthird, anauxili'ary device' is provided hyp-means `ot' which the grindermay be accurately dressed to the proper contour, and its cutting qualilties thus periodically restored. 'For the u'rpose of facilitating thedressing of the w eel it is. desirable that the grindersgbe providedwith not more than one. full convolution of the thread spiral, asin thatcase fa trimmer' diamond 84 ofa'considerable size may be employedwithoutthe danger of interference with the' adjacent threads of thewheel.

As illustrated and described,'the invention@ may be employed in eithermilling or grinding and it is to be understbod,'therefore, that theterms hob, cutting., cutting edge, cutter, etc. as'used in the appendedclaims, are. intended to'describe and apply to either a milling or agrinding tool and to its use in either a milling 01" grinding operation.

`What I claim as-my inventionis l. A rotary gear cutting` tool havingplurality of axially disposed teeth projecting a from a plane face andarrangedto form-an effective operating portion which is of racksectionof constant pitch, each tooth being provided with a top cutting edge and'o posite side -cutting edges, the top cutting e ges all lying in aplane perpendicular -to the axis of the tool andthe corresponding sidecutting edges'of the teeth being equally mclined to said plane,said'vteeth being of equal width,

plane perpendicular to theaxisof the A. gear cutting tool having aplurality of side cutting edges projecting from a lane faceand arrangedin a spiral which is o constant pitch along astraight line offset r'mthe axis ofthe tool.

3.' A gear cutting tool provided with. a

ilo

plurality of cutting `teeth projecting from a' plane face and arrangedto form an effective operating portion of rack sectionl of constantpitch alonga straight line offset from its axis, each tooth beingprovided With-oppof' site side cutting' edges, correspondingside cuttingedges Abeing equally inclined'to a. plane 'perpendicular to the axis ofthe tool and 4said'teeth being of equalwidth in a plane perpendicular tothe axis of thetool.

4. A-rotary gear cuttin tool having a., 1urality of axially djspose.teeth arr to tot' rack section of. constant straight line oiset fromthe axis of the tool,

form an effective operating portion which ispitch along` a each toothbeing provided with opposite side cutting edges, the corresponding sidecutting edges of the teethbeing equally inclined to4 a planeerpendicular to the axis of the tool, said teet i being of equal Widthand o f equal height and having' their outermost points all lying in asingle plane perpendicular to the axis of the tool. Y

5.A gear cutting tool having a plurality of side cutting edges arrangedin a spiral the perpendiculars to which at the pitch surface along astraight line oiiset from its axis intersect in a single point, each ofsaid cutting edges being arranged to finish cut a side face of a geartooth. i

6. A gear cutting tool havinga plurality of side cutting edges arrangedin a spiral the perpendiculars along a straight line oii'setfrom itsaxis intersect in a single point which lies in a line at ,f right anglesto the axis of the tool, each of of teeth arranged in a spiral, eachtooth being said cutting edges being arranged to iinish cut a side faceof a gear tooth.

7. A rotary gear cutting tool Having a plurality of teeth arranged in aspiral of the general involute type each tooth being provided with apair of side cutting edges said teeth being of equal width in a planeperpen-` dicular to the axis of the tool, corresponding side cuttingedges being equally inclined to said plane.

8. A rotary' gear cutting tool having a plurality of teeth arranged in aspiral of the general involute type, each tooth being prof vided with atop cutting edge and a pair of side cutting edges, the top cutting edgesall lying in afplane perpendicular to the axis of thetool andcorresponding side cutting edges being equally inclinedl to said plane,said teeth being of equal width and equal' height. 9. A gearcutting toolhaving a plurality of teeth arranged in a spiraL'each tooth being.L

provided with a pair of side cutting edges, said teeth being of equalwidth in a plane per-y pendicular to the axis of the tool and thecorresponding side cutting edges of the teeth being equally inclined tosaid plane.

10. A gear cutting tool having a plurality provided'with a top cuttingedge and a pair of side cuttingy edges', the top cutting edges all lyingin a plane perpendicular to the axis of the tool and corresponding sidecutting edges being equally inclined to said plane,

said teeth being-ot equal width.

11. A gear cutting tool -having a plurality of teeth arranged ina'spiral, each tooth being provided with atop cutting edge and a pairof'side cutting edges, said top cutting edges all lying' in aplane'per'pendicular to the axis of the tool and corresponding sidecutting edges being equally inclined to said plane,

of equal width and equal hei to which at the `pitch surface said teethbeing of equal width and vequal height.

12.', A gear cutting tool having a plurality ',of teeth arranged in aspiral o-the modified involute type, each tooth being provided with atop cutting edge and a pair of side cutting edges, the top cutting edgesall `lying in a plane perpendicular to the axis of the tool and a pairof side ctting v plane perpendicular to the axis of the tool and l lcorresponding side cutting edges being equally inclined to said plane,sald teeth being t. 14. A hob comprising a ody having a series ofteeth"projecting laterally from one face thereof, said hob being of thecrown wheel type having the teeth spirally arranged about the center toform a plurality of convolutions of the modiiied involute type.

15. A crown hob consisting of a diskshaped body and a plurality ofspirally aligned cutting edges, in which theialignment of cutters isalong a'modilied involute of circle, the spac.

ing of spirals is .uniform along a straight line oifset from the centerof hob, and the angle of intersection of the cutting spirals with saidstraight line is acuteyeach of said cutting edges being arranged tolfinish cut a side face of a gear tooth.

f 16; A crown hob of ,theLextended involute i crown type having a diskshaped body and spirally wound cutting teeth, having a base radinsselected with reference to the pitch,

and a modification selected with reference to thehelix angle of theWorms to be generated.

17. A crown hob for generation of'worlns having its cutting edgesarranged in a spiral resulting from a uniform translation along astraightline situated at a fixed distance from the center of the hob,and a uniform rotation about said center, said fixed distance being thealgebraic sum of a base radius, and a modification, and the relationbetween the two components being such that the circumference of the basecircle is exactly equal to a multiple of the pitch of, the worms, andthe modification depends upon the helix angle of the worms to begenerated. s

18. A gear cutting, tool having its cut-ting edges projecting from aplane face Vand arranged in the formof a plurality of convoli1- tionsthe pitch ofwhiclris uniform along a straight line oset, from'the axisof the tool and which intersects said line at an ever increasing. acuteangle, each' of said cutting edges beingarranged to finish cut a sideface of a gear tooth.

19. A rotary gear cutting tool having a plui rality of Acutting" teethextending'ina direction generally parallel to the axis vof the tool andarranged ina s iral of constant pitch along a straight line o set from.said axis, the outerilnost'l points of the cuttingl teeth lying in aplane perpendicular to said axis.

20. AA rotary vgear cutting tool having a plurality of cutting teethextendin in a direction generally'parallel to the axis of the tool andarranged 1n a spiral'of constant pitchv along a straight line offsetfrom said axis,

said-teeth being of equal height and having their outermost points alllying in a single plane perpendicu ar to the axis of the tool.

21. A rotary gear cutting tool havinga pluf `rality of teeth extendingin the general direction of its-'axis and arranged in a spiral'of con-lstant pitch, along a straight line offset from said axis, each 'toothbeing provided with 'af pair of side cutting edges, the teeth being of'f equal Width in 4'a'plane perpendicular to the axis of the tool andcorrespondin' side cutting edges of the teeth being equal y inclined tothe laxis of the tool.

22. A rotary gear cutting tool having aplurality of teeth extending inthe general direction of its axis and arranged in a spiral of constantpitch.' along a. straight line offset from Said axis, ash tooth beingpfovided with a pair' of side cuttin edges, the teeth Vbeing of equalheight and o equal width, corresponding side cutting edges of the'teethbeing equally inclined to axis. 23. A rotary tool, having'an operatingportion extending in the general direction of its axis, the oppositeside cuttin edges of which are arranged along spirals w ich are ofconstant pitch along a straight line offset from the axis of the tool,said spirals being equally spaced from each other throughout their planeperpendicular to the axis of ranged in yarow' which extends around theaxis of thecutter in a' spiral curve which has a uniform lea@- along 4aline tangent to a circle which has itsl center at the axis of thecutter. In testimony whereof I aiiix my signature..1

NIKOLA TRBOJEVICH.

